1. Field of the Invention
The present invention relates to a computer program for the particle method in a broad sense, in which objects are modeled into (or using) particles whose displacements and/or deformations can be calculated, if necessary, considering transmission (or exchange) of force, heat or material between the touched particles.
2. Description of Related Art
In the finite element method (FEM), mainly physical relations between the elements are described as relations between the nodes by dividing the continuum into piecewise elements enclosed with the nodes. Therefore, analysis of a contact-involving problem using FEM requires treatment. For example, the treatment is a procedure to calculate force to compensate the element overlap (Japan Pat. No. 2,692,668), generating new elements between the touched surfaces (Japan Pat. No. 3,242,811), or imaging a touching plane with the averaged normal direction of both front planes on both elements (Japan Pat. Application No. 2001-27,470).
However, FEM using the treatment is fundamentally unsuitable for a dispersed system, because FEM is naturally for the continuum and treats partial contact between discontinued elements. Moreover, for instance with rectangular solids, the contact has various modes of not only plane-to-plane, but also plane-to-corner, ridge-to-ridge, and transition between them. Therefore, it is difficult to take account of these complex modes using FEM.
On the other hand, the particle method is fundamentally suitable for an analysis of a dispersed system. However, the particle shape is limited in sphere or no shape at present (for example, “Particle method”, S. Koshizuka, 2005,, Maruzen, Tokyo, in Japanese). Therefore, there is a problem of requiring a large number of particles in modeling of a complicated shape using the particle method particularly in three dimensions (3D). Moreover, even if a large number of particles are used, there is a problem in that microscopic shape of the particles is remained and decides microscopically the contacting direction between assemblies of the particles.
In the mesh-free method, U.S. Pat. No. 6,718,291, discloses representing a geometry using implicit functions, representing the boundary conditions using similar functions, and solving coefficients of interpolating functions between these functions. However, the mesh-free method is based on the continuum and difficult to apply to a strongly nonlinear problem or shape changes.